Yep. Case: ~$70ish, MB: ~$150is-200ish, RAM: ~<$115ish, CPU: ~$120ish
It wouldn't be a powerhouse but would be a decent computer nonetheless
Edit:
Forgot the PSU. You'll be pushing $450-500 then from my quick and dirty numbers
First off, you NEED a PSU, or the computer you build won't turn on. PSU = Power Supply Unit. That thing which provides electricity to the rest of your hardware. And for that matter, any decent system builder recognizes that the PSU is the foundation of a solid, stable system. An otherwise top-end system with a crappy generic PSU will not only run like a much lesser system, but will likely be a timebomb waiting to explode...
Take it from me, as I am not only a professional computer repair technician by trade, but am also a guy who learned VERY early in his PC building career the difference between a good PSU and a not-so-good PSU.
My very first ever custom build was killed by the generic PSU which came with the case I bought, and when it died, it took hostages: My motherboard, CPU, RAM, and the $450 VGA card (which just happened to be the most powerful card on the market at the time I bought it) followed the PSU out in a blaze of glory. Nearly $1000 of that rig gone.
Each of the two subsequent gaming rigs I have built myself, I have invested hours of research into finding the best brands and models of PSU, and will typically budget more for a solid power supply than for any other component, with the exception of the CPU and graphics card. That investment has paid off, as I can unpack system number two from it's spot in my closet, plug it in, and it will purr, despite being over ten years old now. My current gaming rig, only a year and a half old, sees nearly daily use, runs stable at all times, and can chew through a 12+ hour session of Skyrim on 1920x1080 with everything on ultra, and not even a momentary drop in framerate to blemish that time. You simply DON'T get that sort of performance and stability without the solid electrical control of a reliable power supply...
If I had $400 to spend on a custom build, here is what I would buy:
-$200 power supply
-$200 motherboard
-save over the next year or so for the rest of the parts...